1/15
00:00

F.1 Estimating differences by rounding

Loading questions...

What does it mean to estimate by rounding?

Estimating by rounding means finding an answer that is close to the exact answer, but easier and faster to calculate. We round numbers to the nearest place value (like 10, 100, or 1,000) before subtracting, so the subtraction is simpler.

Example:
  • 643 βˆ’ 278 is tricky. But if we round: 640 βˆ’ 280 = 360, which is a quick estimate.
Note

Estimation does not give the exact answerβ€”it gives a close answer that helps us check reasonableness or solve problems quickly.

How do you round numbers?

To round a number, look at the digit to the right of the place value you are rounding to. If it is 5 or more, round up. If it is less than 5, round down.

Steps:
  • Round 3,476 to the nearest hundred.
  • Look at the tens digit (7). It is 5 or more.
  • So, round 3,476 up to 3,500.
Note

Always check which place value you are rounding to: tens, hundreds, thousands, or higher.

How to estimate a difference by rounding

To estimate a subtraction problem, first round both numbers to the same place value. Then subtract the rounded numbers to get an estimated difference.

Example:
  • 4,862 βˆ’ 3,179
  • Round both numbers to the nearest thousand: 5,000 βˆ’ 3,000 = 2,000
  • The estimated difference is about 2,000.
Note

Rounding to different place values (10, 100, 1,000, 10,000, 100,000) will give different estimates. Choose the place value that makes sense for the situation.

Examples with different place values

Here are examples of estimating by rounding to different place values.

Examples:
  • 8,746 βˆ’ 3,298 β†’ nearest ten: 8,750 βˆ’ 3,300 = 5,450
  • 8,746 βˆ’ 3,298 β†’ nearest hundred: 8,700 βˆ’ 3,300 = 5,400
  • 8,746 βˆ’ 3,298 β†’ nearest thousand: 9,000 βˆ’ 3,000 = 6,000
Note

Notice how the estimate changes depending on the place value you round to. Rounding to a larger place value makes the estimate less exact but faster.

When should you estimate?

Estimation is useful when you want a quick answer, to check if an exact answer makes sense, or when exact details are not required.

Examples:
  • Estimating the cost of groceries before checkout.
  • Checking if your subtraction answer is reasonable.
  • Figuring out about how many miles are left on a trip.
Note

Estimation is about being close enough, not exact. Use it for speed, reasonableness, and problem-solving.